Question

If two liquids of same mass but densities ${\rho }_1$ and ${\rho }_2$ respectively are mixed, then the density of the mixture is:

• A. $\rho =\frac{{\rho }_1+{\rho }_2}{2}$
• B. $\rho =\frac{{\rho }_1+p_2}{2{\rho }_1{\rho }_2}$
• C. $\rho =\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$
• D. $\rho =\frac{{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$

Answer 1

The correct option is C $\rho =\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$

For 1st liquid, mass $=m$ and density $={\rho }_1$

For 2nd liquid, mass $=m$ and density $={\rho }_2$

Total volume of the mixture $=m(\frac{1}{{\rho }_1}+\frac{1}{{\rho }_2})$

When both are mixed, the density of the mixture will be

$\rho =\frac{2m}{m(\frac{1}{{\rho }_1}+\frac{1}{{\rho }_2})}=\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$